Period-Doubling Bifurcation of Cycles in Retarded Functional Differential Equations
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Dynamics and Differential Equations |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1007/s10884-023-10249-3 |
| Doi | http://dx.doi.org/10.1007/s10884-023-10249-3 |
| Keywords | Retarded functional differential equation; Delayed differential equation; Period-doubling bifurcation; Fredholm operator; Lyapunov-Schmidt reduction |
| Description | A rigorous description of a period-doubling bifurcation of limit cycles in retarded functional differential equations based on tools of functional analysis and singularity theory is presented. Particularly, sufficient conditions for its occurrence and its normal form coefficients are expressed in terms of derivatives of the operator defining given equations. We also prove the exchange of stability in the case of a non-degenerate period-doubling bifurcation. The approach concerns Fredholm operators, Lyapunov-Schmidt reduction and recognition problem for pitchfork bifurcation. |
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